Exercises on Partial Derivatives

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  • #1
MathematicalPhysicist
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here there are Exercises on Partial Derivatives: http://www.uAlberta.ca/dept/math/gauss/fcm/calculus/multvrbl/basic/partl_drvtvs_exrcss/partl_dervtv_exrcss.htm
can comeone please solve the first two problems (for some reason i can't read the answers).
my answers:
1. 3(3xy-4y^2)^2(3x-8y)
2. y/(x+y)^2

thanks in advance.
 
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  • #2
You are correct.
 
  • #3
Hooray for the University of Alberta!
 

What are partial derivatives?

Partial derivatives are a type of mathematical function that calculates the rate of change of a multivariable function with respect to one of its variables, while holding all other variables constant.

Why are exercises on partial derivatives important?

Exercises on partial derivatives are important because they help us better understand how a multivariable function changes with respect to its individual variables, which has many real-world applications in fields such as physics, economics, and engineering.

What is the process for finding a partial derivative?

The process for finding a partial derivative involves treating all variables except the one in question as constants, then using basic derivative rules to find the derivative of the function with respect to the variable in question.

How are partial derivatives used in optimization problems?

Partial derivatives are used in optimization problems to find the maximum or minimum of a multivariable function by setting its partial derivatives equal to zero and solving for the critical points.

What are some common mistakes made when solving exercises on partial derivatives?

Some common mistakes made when solving exercises on partial derivatives include forgetting to treat all variables except the one in question as constants, using the product rule incorrectly, and forgetting to include the chain rule when dealing with composite functions.

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